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arXiv:2201.04258 · Physical review. B./Physical review. B

Magnetic phase transition in disordered interacting Dirac fermion systems via the Zeeman field

Jingyao Meng, Lufeng Zhang, Tianxing Ma, Haiqing Lin

Published May 18, 2022• 2 citations
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Abstract

Using the determinant quantum Monte Carlo method, we investigate the antiferromagnetic phase transition that is induced by the Zeeman field in a disordered interacting two-dimensional Dirac fermion system. At a fixed interaction strength $U$, the antiferromagnetic correlation is enhanced as the magnetic field increases and, when the magnetic field is larger than a ${B}_{c}(U)$, the antiferromagnetic correlation shall be suppressed by the increased magnetic field. The impact of Zeeman field $B$, Coulomb repulsion $U$, and disorder $\mathrm{\ensuremath{\Delta}}$ is not isolated. The intensity of magnetic field effect on the antiferromagnetic correlation shall be strongly suppressed by disorder. Differently, it will be promoted by weak interaction, but, when $U$ becomes larger than ${U}_{c}=4.5$, the increased interaction will suppress the intensity of this effect and here ${U}_{c}=4.5$ coincides with the critical strength inducing the metal-Mott insulator transition in a clean system. Moreover, at a fixed magnetic field $B$, strong interaction shall suppress the antiferromagnetic phase rather than promote it.

DOI
10.1103/physrevb.105.205121

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Using the determinant quantum Monte Carlo method, we investigate the antiferromagnetic phase transition that is induced by the Zeeman field in a disordered interacting two-dimensional Dirac fermion system. At a fixed interaction strength UUU, the antiferromagnetic correlation is enhanced as the magnetic field increases and, when the magnetic field is larger than a Bc(U){B}_{c}(U)Bc​(U), the antiferromagnetic correlation shall be suppressed by the increased magnetic field. The impact of Zeeman field BBB, Coulomb repulsion UUU, and disorder \ensuremathΔ\mathrm{\ensuremath{\Delta}}\ensuremathΔ is not isolated. The intensity of magnetic field effect on the antiferromagnetic correlation shall be strongly suppressed by disorder. Differently, it will be promoted by weak interaction, but, when UUU becomes larger than Uc=4.5{U}_{c}=4.5Uc​=4.5, the increased interaction will suppress the intensity of this effect and here Uc=4.5{U}_{c}=4.5Uc​=4.5 coincides with the critical strength inducing the metal-Mott insulator transition in a clean system. Moreover, at a fixed magnetic field BBB, strong interaction shall suppress the antiferromagnetic phase rather than promote it.
We use the determinant quantum Monte Carlo method (DQMC) to study the interaction-driven semimetal to antiferromagnetic insulator transition in a $\ensuremath{\pi}$-flux Hamiltonian with modulated hoppings, a model which has two species of Dirac fermions. It is found that the critical interaction strength Uc{U}_{c}Uc​ is decreased by reducing the velocity of the outer Dirac cone, while the inner cone velocity fixes the bandwidth. Although Uc{U}_{c}Uc​ is monotonic, at fixed inverse temperature $\ensuremath{\beta}$ the antiferromagnetic (AF) structure factor has a maximum as a function of the hopping modulation. We also study the corresponding strong coupling (Heisenberg model) limit, where the sublattice magnetization is enhanced by the alternation of the exchange couplings. The AF order is shown to be nonmonotonic, and maximal at an intermediate degree of anisotropy, in qualitative agreement with the Hubbard model. These results quantify the effect of the velocities on the critical interaction strength in Dirac fermion systems and enable an additional degree of control which will be useful in studying strong correlation physics in ultracold atoms in optical lattices.
Using the determinant quantum Monte Carlo method, we investigate the metal-insulator transitions induced by the stripe of charge density in an interacting two-dimensional Dirac fermion system. The stripe will introduce the transport anisotropy and insulating intermediate phase into the system, accompanied by the change of band structure and a peak of density of states around Fermi energy. In the case of strong correlation, stripe exhibits competition with Coulomb repulsion through closing the energy gap and disrupting the magnetic order and finally drives the system in the Mott insulating phase back to the metallic state. Our results may provide a feasible way to modify transport properties by setting charge stripes in experiments.
We numerically study the superconductor-insulator phase transition in a model disordered two-dimensional (2D) superconductor as a function of applied magnetic field. The calculation involves quantum Monte Carlo calculations of the (2+1)D(2+1)\text{D}(2+1)D XYXYXY model in the presence of both disorder and magnetic field. The XYXYXY coupling is assumed to have the form $\ensuremath{-}J\text{ }\text{cos}({\ensuremath{\theta}}_{i}\ensuremath{-}{\ensuremath{\theta}}_{j}\ensuremath{-}{A}_{ij})$, where Aij{A}_{ij}Aij​ has a mean of zero and a standard deviation $\ensuremath{\Delta}{A}_{ij}$. In a real system, such a model would be approximately realized by a 2D array of small Josephson-coupled grains with slight spatial disorder and a uniform applied magnetic field. The different values $\ensuremath{\Delta}{A}_{ij}$ then correspond to an applied field such that the average number of flux quanta per plaquette has various integer values NNN: larger NNN corresponds to larger $\ensuremath{\Delta}{A}_{ij}$. For any value of $\ensuremath{\Delta}{A}_{ij}$, there appears to be a critical coupling constant ${K}_{c}(\ensuremath{\Delta}{A}_{ij})=\sqrt{{[J/(2U)]}_{c}}$, where UUU is the charging energy, below which the system is a Mott insulator; there is also a corresponding critical conductivity ${\ensuremath{\sigma}}^{\ensuremath{\ast}}(\ensuremath{\Delta}{A}_{ij})$ at the transition. For $\ensuremath{\Delta}{A}_{ij}=\ensuremath{\infty}$, the order parameter of the transition is a renormalized coupling constant ggg. Using a numerical technique appropriate for disordered systems, we show that the transition at this value of $\ensuremath{\Delta}{A}_{ij}$ takes place from an insulating (I) phase to a Bose glass (BG) phase, and that the dynamical critical exponent characterizing this transition is $z\ensuremath{\sim}1.3$. By contrast, z=1z=1z=1 for this model at $\ensuremath{\Delta}{A}_{ij}=0$. We suggest that the superconductor-to-insulator transition is actually of this I to BG class at all nonzero $\ensuremath{\Delta}{A}_{ij}$'s, and we support this interpretation by both numerical evidence and an analytical argument based on the Harris criterion [A. B. Harris, J. Phys. C 7, 1671 (1974)]. Kc{K}_{c}Kc​ is found to be a monotonically increasing function of $\ensuremath{\Delta}{A}_{ij}$. For certain values of KKK, a disordered Josephson array may undergo a transition from an ordered, Bose glass phase to an insulator with increasing $\ensuremath{\Delta}{A}_{ij}$.
We use determinant quantum Monte Carlo simulations to study the role of electron-electron interactions on three-dimensional (3D) Dirac fermions based on the $\ensuremath{\pi}$-flux model on a cubic lattice. We show that the Hubbard interaction drives the 3D Dirac semimetal to an antiferromagnetic (AF) insulator only above a finite critical interaction strength and the long-range AF order persists up to a finite temperature. We evaluate the critical interaction strength and temperatures using finite-size scaling of the spin structure factor. The critical behaviors are consistent with the (3+1)-dimensional Gross-Neveu universality class for the quantum critical point and 3D Heisenberg universality class for the thermal phase transitions. We further investigate correlation effects in the birefringent Dirac fermion system. It is found that the critical interaction strength Uc{U}_{c}Uc​ is decreased by reducing the velocity of the Dirac cone, quantifying the effect of velocity on the critical interaction strength in 3D Dirac fermion systems. Our findings unambiguously uncover correlation effects in 3D Dirac fermions and may be observed using ultracold atoms in an optical lattice.
We study the effects of disorder on long-range antiferromagnetic correlations in the half-filled, two-dimensional, repulsive Hubbard model at T=0.T=0.T=0. A mean field approach is first employed to gain a qualitative picture of the physics and to guide our choice for a trial wave function in a constrained path quantum Monte Carlo (CPQMC) method that allows for a more accurate treatment of correlations. Within the mean field calculation, we observe both Anderson and Mott insulating antiferromagnetic phases. There are transitions to a paramagnet only for relatively weak coupling, U<2tU<2tU<2t in the case of bond disorder, and U<4tU<4tU<4t in the case of on-site disorder. Using ground-state CPQMC we demonstrate that this mean field approach significantly overestimates magnetic order. For U=4t,U=4t,U=4t, we find a critical bond disorder of ${V}_{c}\ensuremath{\approx}(1.6\ifmmode\pm\else\textpm\fi{}0.4)t$ even though within mean field theory no paramagnetic phase is found for this value of the interaction. In the site disordered case, we find a critical disorder of ${V}_{c}\ensuremath{\approx}(5.0\ifmmode\pm\else\textpm\fi{}0.5)t$ at U=4t.U=4t.U=4t.
Using exact quantum Monte Carlo calculations, we examine the interplay between localization of electronic states driven by many-body correlations and that by randomness in a two-dimensional system featuring linearly vanishing density of states at the Fermi level. A novel disorder-induced nonmagnetic insulating phase is found to emerge from the zero-temperature quantum critical point separating a semimetal and a Mott insulator. Within this phase, a phase transition from a gapless Anderson-like insulator to a gapped Mott-like insulator is identified. Implications of the phase diagram are also discussed.